Question

a student says that dilation with a scale factor of $\frac{1}{2}$ will make the image congruent to the original. do you agree? explain your reasoning.

Explanation:

Congruent figures have the same size. Dilation with a scale factor of $\frac{1}{2}$ changes the size of the original figure (makes it smaller). So the image and the original cannot be congruent.

Answer:

No, I do not agree. A dilation with a scale factor of $\frac{1}{2}$ changes the size of the original figure. Congruent figures must have the same size. Since the size is altered (reduced by half), the image is not congruent to the original.